A 3dB increase in volume requires a doubling of Watts.

There is a 6dB loss in volume for every doubling of distance.

If I have a 99dB sensitivity speaker at 1 watt, 1 meter, and I want to know how many watts my power amp will need to deliver in order to be CAPABLE of achieving 105 dB at 4 meters, I would take the 99dB, reduce it by 6 at 2 meters, and another 6 at 4 meters. Now I have 87dB at 4 meters, and 1 watt. Climbing back up, I get to 90dB with 2 watts, 93dB with 4 watts, 96dB with 8 watts, 99dB with 16 watts, 102dB with 32 watts, and finally 105dB at 64 watts, right? So if I wanted a power amp to have a doubling headroom, Iād be looking for an amp with at least 124 watts/ch. Is this correct?

If I am understanding that correctly, then things get weird with, for example, a 90dB sensitivity speaker. -12dB at 4m = 78dB. This builds up to 512 watts needed for the same 105dB volume, and suggesting a power amp of minimum 1024 watts/ch. to give doubling headroom.

Sorry for this long question and likely bad math/understanding; Iām new to this hobby.

I believe your calcs are correct, but I think your doubling-for-headroom requirement is not at all a requirement, unless youāre trying to deafen yourself in one listening sessionā105 dBA is VERY loud already.

This doesnāt take into account the reverberant field of the room. What youāre describing would be true in half space (with a speaker in the middle of a basketball court), but you get less than a full 6 dB loss (per doubling if distance) in-room.

Thanks Chris, that makes perfect sense. Is there a way then to approximate how many watts your amp will need to deliver, to achieve a proposed dB level, at a certain listening distance, with a certain sensitivity speaker, in a given volume of space? I know thatās convoluted, but do you see where Iām coming from? āThis is the size of my room, I sit this far away from the speakers, they are this sensitivity, to get them to āXā dB I need āYā watts(ish).ā
Thanks again, I appreciate you having taken the time to respond.

The issue with this analysis and discussion, which seems to be repeatedly coming up on the forum, is the underlying assumption (maybe it isnāt an assumption and Iām reading too much into this topic) that weāre talking about sustained power for peaks of up to 105 dB.

We arenāt. Intense peaks of that magnitude in the concert hall are just that, peaks. A correct perspective on this is how much dynamic headroom an amp has or would need. Note the emphasis on ādynamicā. An amp rated at, say, 250 watts/ch sustained output isnāt necessarily incapable of delivering brief bursts of higher power when the material calls for it. Spec sheets very rarely (ever?) cite dynamic headroom. Which is why addressing this question is so frustrating. It also suggests an important gap in how manufacturers measure and spec amplifiers. Iām not entirely sure an industry recognized standard even exists for that type of measurement.

I genuinely understand your frustration. There do seem to be a lot of us out here who are confused on the topic; thatās why Iām hoping someone can help me understand it a bit more. The reason I put the word ācapableā in all caps on my post was to emphasize exactly that. I never listen to music at that volume or anywhere near it, but we seem to often discuss how many watts an amp is capable of producing, but doesnāt that have a direct relationship to how loud that amp could make a certain sensitivity speaker play to a certain point in a room? Thatās what Iām trying to understand better. I know the answer seems to always be, ājust get the most powerful amp you can affordā, but it would be nice to know how many watts you really would need.

Yes. Absolutely. And with the notable exception of certain panel speaker designs, conventional driver speakers present a complex load that can vary a lot over frequency. Power delivery to the speaker will be a function of frequency. As has been discussed elsewhere, typical practice is to measure and quote power delivery only at 1 kHz (including PSA). So that is another significant gap in manufacturer datasheets in addition to dynamic headroom.

It sounds like you are talking THX specs. Specifically the THX Ultra and Ultra2 range of products. You should probably be talking to a certified THX installer about your situation.

Very few audiophiles would require such SPLs. The only audiophile speaker manufacturer I have seen mention maximum output levels is Magico.

You are more likely to run into mechanical limitations of the speaker, especially at lower frequencies. If you are trying to figure out how small an amplifier you can get away with, you are on the wrong forum.